考虑治疗因素的埃博拉病毒模型的研究
Research on an Ebola Virus Model Considering Therapeutic Factors
DOI: 10.12677/aam.2026.154196, PDF,   
作者: 李昕瑞：兰州理工大学理学院，甘肃 兰州
关键词: 埃博拉病毒；医院病床数；后向分支；SIHRD模型；Ebola Virus； Hospital Beds； Backward Bifurcation； SIHRD Model
摘要: 埃博拉病毒的传播威胁着人类的生命安全。为了更全面地分析埃博拉病毒传播对人类造成的影响，建立了一类考虑空床位影响、感染饱和效应和住院率的易感–传染–住院–康复–死亡(SIHRD)传染病模型。首先，证明了解的正性、有界性以及无病平衡点的稳定性，并对地方病平衡点的存在性进行分析。随后，推导出发生正向分支和后向分支的条件。此外，证明了当医院容纳量较大时会产生前向分支，当医院容纳量较小时会出现后向分支。最后，通过数值模拟验证理论结果，并给出控制病毒传播的相关建议。
Abstract: The spread of the Ebola virus poses a threat to human life safety. To conduct a more comprehensive analysis of the impact of the Ebola virus transmission on humans, a susceptible-infectious-hospitalized-recovered-dead (SIHRD) infectious disease model considering the influence of vacant beds, infection saturation effect and hospitalization rate was established. Firstly, the positivity, boundedness of the solution and the stability of the disease-free equilibrium point were proved, and the existence of the endemic equilibrium point was analyzed. Subsequently, the conditions for the occurrence of forward and backward bifurcations were derived. Moreover, it was proved that a forward bifurcation would occur when the hospital capacity is large, and a backward bifurcation would occur when the hospital capacity is small. Finally, the theoretical results were verified through numerical simulation, and relevant suggestions for controlling the virus transmission were given.
文章引用：李昕瑞. 考虑治疗因素的埃博拉病毒模型的研究[J]. 应用数学进展, 2026, 15(4): 718-734. https://doi.org/10.12677/aam.2026.154196

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